$B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 4x + 1$ and $ BC = 9x - 9$ Find $AC$.
Explanation: A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {4x + 1} = {9x - 9}$ Solve for $x$ $ -5x = -10$ $ x = 2$ Substitute $2$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 4({2}) + 1$ $ BC = 9({2}) - 9$ $ AB = 8 + 1$ $ BC = 18 - 9$ $ AB = 9$ $ BC = 9$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {9} + {9}$ $ AC = 18$